Quartz piezo-electric element



Patented Dec. 15, 1936 UNITED STATES PATENT OFFICE Samuel A. Bokovoy, Audubon, N. J., assigner to Radio Corporation of America, a corporation of Delaware Application May 31, 1934, Serial No. 728,377

13 Claims.

This invention relates to the piezo-electric art and to the cutting of quartz crystal elements sultable for use in an oscillating circuit. More particularly, my invention is concerned with the making and use of such elements as are intended to be vibrated at a width-mode frequenecy, or at a frequency which is for the most part dependent upon that one of the two greater dimensions of the crystal which is measured along a Y-axis.

A principal object of my invention is to provide a piezo-electric crystal element that will oscillate efficiently at only one Width-mode frequency.

Another object of my invention is to provide a process for cutting such a crystal element so that of several frequency modes at first present only one will remain after finishing the grinding process.

Another object of my invention is to provide a simple, inexpensive and efficient mode of procedure in the cutting of crystals to eliminate as far as possible any uncertainties with regard to the oscillatory characteristics of the crystal element when nished.

Other objects and advantages of the invention will become apparent from the following description taken in connection with the accompanying drawing in which Figure l is a diagrammatic view looking at a so-called X-cut quartz crystal section when projected with the optic axis perpendicular to the plane of projection;

Fig. 2 is a graphic chart showing the relation between the length of a crystal along the optic axis and the frequency constant thereof, and illustrating how crystals of like width but of different lengths may be caused to oscillate to produce any one or more of three width-mode frequencies; and

Fig. 3 is another graphic chart indicating illustratively certain of the relations between length, width, frequency constant and normal widthm'ode frequency of quartz crystals cut in accordance with my invention.

It is a recognized fact, which has been borne out by my research work, that, when a quartz crystal is X-cut", that is to say, when it is cut into a rectangular plate so oriented with respect to the mother crystal that its thickness dimension is along an electric axis and its length along an optic axis, several modes of vibration and consequently several normal frequency responses are possible of attainment even when the crystal is employed in a non-regenerative circuit. One of these modes of vibration, namely the thickness mode, is always present, but, because this frequency is so much higher than any of the widthmodes, it is not within the scope of my invention to eliminate the thickness mode. Usually the circuit for which a crystal is intended to vibrate at a width-mode frequency wil have no tendency to excite the same at its thickness frequency.

Where more than one width-mode oscillatory characteristic is present in a crystal, difculties sometimes arise because the several modes are not very far apart. It is then possible to tune the tank circuit to any one of these frequencies. In certain instances, two of these lower modes of vibration may be within kilocycles or so of each other. Instances have arisen where, due to a slight misadjustment of the tuning circuit, two of the width-mode frequencies of the crystal would appear simultaneously.

It is well known in the art that the conditions above referred to are frequently to be met, but, so far as is known to the applicant, no solution has heretofore been presented such as would provide for a consistent production of crystal elements having only one width-mode freedom of oscillation.

In general I have found that satisfactory results can be obtained by choosing a suitable width for the crystal in accordance with the desired frequency and in accordance with the formula K W- f (l) The frequency is here expressed in megacycles, the width w in mils, or thousandths of an inch, and the value of K is a function of the length, as will be observed by reference to Fig. 2. It is the practice to start with a blank both the width and length of which are smoothed up to slightly greater dimensions than those to which it will be finished. The natural frequency then obtained should be about 1% to 2% lower than the desired frequency. The length will be approximately 50% greater than the width, assuming that the crystal is to be finished for the so-called normal width-mode freedom of oscillation. At this point it is best to begin reducing the length and to check the frequency at intervals between the grinding operations. Since the width will remain unchanged, the values of K and of f will be increased proportionately. By continuing to reduce the length without further reducing the width, not only will the frequency be brought up to the desired value, but the upper frequency mode will disappear.

To give a concrete example of how a crystal plate may be cut for normal width-mode vibration at 200 kilocycles, it is preferable to start with a blank having a width of approximately .565" and a length of say .85. Such a crystal will have two low frequency modes at around 196 kilocycles and 237 kilocycles and the values of K will be in the neighborhood of 111 and 132 respectively. Now, if the length is gradually reduced, these frequencies and constants will increase, since K equals fw and the width is not being changed.

On reducing the length, a point will be reached where the upper frequency becomes so weak as to be scarcely noticeable. This occurs when the constant for the upper frequency reaches a value of approximately 133. The constant for the lower frequency will then be about 112.

With somewhat further reduction of the length, the desired frequency rating 200 kilocycles may be obtained. At this frequency the so-called upper-mode freedom of oscillation can not be brought back, regardless of what the tuning of the tank circuit may be. The explanation seems to be that a quartz crystal will not support a frequency constant K having a value above 135.

It will be understood that the specific cases of normal-mode frequencies shown in Fig. 3 in their relation to length and width are by no means indicative of any limits of frequency possible of attainment when my invention is carried out. The graph could be extended to include crystals of greater dimensions and crystals having a single Y-mode frequency response at other than the so-called normal mode.

Occasionally it may be desired to cut a crystal suitable for vibration at no other than the lower-mode frequency. rIhe characteristics of such a crystal are in no wise indicated in Fig. 2 which covers only a certain range of correlation of length to frequency constant wherein the lower mode frequency, if it is present, accompanies the normal mode. The lower-mode frequency can be obtained exclusively, however, by making the dimension along the Z-axis the width dimension and choosing a value for the dimension along a Y-axis such that this Y-dimension or length becomes the principal factor indetermining the frequency. This relationship can best be explained by the formula L= (2) where has the same significance as given in Formula (1) and Ly is the length in mils along a Y-axis.

Without attempting to explain the natural laws governing the limits of values to be assigned to the frequency constant K and to the ratios of length to width for obtaining a single frequency response, to the exclusion of other width-mode responses, it may be well to give below the chara-cteristics of certain specific specimens of piezo-electric plates which I have carefully measured and tested, and let the facts speak for themselves. Others skilled in the art will, no doubt, be able to extend the range of characteristic correlations for producing oscillator elements having single-frequency responses. rEhe range of possibilities in this respect has by no means been exhaustively explo-red, although I have found that there are available even more than the three modes of vibration represented in Fig. 2, as will be seen in the following tabulation,

wherein the specimens cataloged are in every case naturally resonant to but one frequency other than the thickness frequency:

Dimensions (mils) along the axes PMO Con- Kilo- Mode lv stent cycles K f X Y Z 1 (Low) 169 2120 1041i 492 106.0 50 D0 135 1145 7i() 616 103. l 96 Do 123 1030 678 .65S 103. 0 100 2 (Normal) 147 760 1110 1. 46 11-1. 0 150 D 124 650 1000 1. 51 113. 7 175 186 562 ST1 l. 55 111.3 10S 119 572 S51 1. 40 11-1. 4 200 186 562 S42 l. 50 11i. 6 201 186 562 820 1. i6 115. 8 206 186 562 704 l. 41 116. 9 208 186 562 764 1. 36 11S. 0 210 148 536 1166 2.18 119. 0 222 8S 523 1113 2.13 120. 8 231 50 415 823 1. 98 116. 2 280 149 570 1563 2. 74 123. 7 217 124 514 1481 2. SS 121. 3 236 136 420 1212 2. S9 122. 2 291 S3 300 1113 2. 85 120. 9 310 60 341 S23 2. 41 119. fl 350 88 370 1.113 3. 0S 122. 8 332 133 312 1030 3. 33 120.1 365 50 294 823 2. 80 121. 7 414 In order that a piezo-electric plate may be depended upon to vibrate at a single Y-axis mode frequency only and at any of the modes above the normal mode, the limits of values to be assigned to the constant K and to the ratio Z/Y have not been generally determined, but in the following instances it has been found that the frequencies stated are single frequencies only within the limits given:

Mode cycles Limits 01K Llml 0f 231 118.0-123-4 2.118-1 Si) 2S() 114. 9-118. 1 2. (1S-1 94 310 11S. 2-123. 3 2. 03-2 70 35o 11m-120.1 2te-2 1o I have explored the possible effect of thickness variations upon the frequency characteristics of a plate which vibrates according to one of its width-modes and have found that the effect upon frequency of thickness variations is almost negligible. There is, however, a notable difference in the strength of oscillations produced by crystals having the same shape of their electrode faces but a difference between their thicknesses. The optimum thickness does not appear to be predictable because it varies with different specimens of the mother crystal.

It is the usual practice to nish a crystal plate with its edges slightly beveled so as to avoid chipping. The extent to which the edges are beveled has more effect upon the width-mode frequency than the thickness. The amount of material removed along the longitudinal edges determines to a considerable extent the effective width.

Although I have disclosed herein certain specic ways and means for accomplishing the objects of my invention, it will be understood that they have been given merely by way of example and should not be construed as limitations to the scope of my invention. Neither is it to be understood that any statements herein made in regard to the values or relationships between dimensions and frequency are other than approximate. It is well known in the art that in order to obtain the frequency characteristics of a piezo-electric plate with the precision that is required, frequent tests of frequent characteristics between successive stages of the grinding operation should be made. My invention, therefore, is not to be limiited except insofar as is necessitated by the prior art and by the spirit of the appended claims.

I claim as my invention:

1. A piezo-electric quartz element having its electrode faces lying in planes substantially parallel to the Y- and Z-axes, and having its length and width so proportioned to one another that it will oscillate at one only of several widthmodes normally possible when a random relation exists between length and width.

2. A piezo-electric quartz element free to oscillate at one Y-axis-mode-frequency only, said frequency in megacycles being equivalent to between where w equals the dimension of the element along a Y-axis, reckpned in thousandths of an inch.

3. An X-cut quartz piezo-electric element having a Y-axis-mode frequency constant of between 103 and 124.

4. An X-cut quartz piezo-electric element having a Y-mode frequency constant of between 103 and 110 and having a dimension along the optic axis such that the element will sustain Y- mode oscillations at one frequency only.

5. A piezo-electric crystal in accordance with claim 4 and wherein the ratio of the dimension along the optic Z-axis to that along the mechanical Y-axis is less than substantially .7.

6. An X-cut quartz piezo-electric element having a width-mode frequency constant of between 111 and 118 and having a length such that it will sustain width-mode oscillations at one frequency only.

7. An X-cut quartz piezo-electric element having a width-mode frequency constant of between 116 and 124 and having a, length such that it will sustain width-mode oscillations at one frequency only.

8. The method of cutting a quartz crystal element so as to exhibit a Y-aXis-mode piezo-electric characteristic at one frequency only which comprises cutting a slab with its electrode faces perpendicular to an electric axis and parallel to the optic axis, reducing the dimension along the Y-axis to such value that it will oscillate at a predetermined Y-axis-mode frequency lower than the desired frequency, and reducing the dimension along the optic axis until the desired frequency is obtained.

9. The method of cutting a quartz piezo-electric element having a single width-mode frequency response which comprises forming a, blank the thickness of which is measured along an electric axis and perpendicular to the optic axis, reducing the width of said blank, measured along a Y-axis, to a desired value and reducing the length, measured along an optic axis until the desired width-mode frequency appears and other width-mode frequencies disappear.

10. The mode of making a quartz piezo-electric element having a single frequency response the value of which is a function of the width and length, which method comprises cutting a slab to such dimensions as will produce an approximate but somewhat lower frequency than that desired, holding the dimension along a, Y-axis to a value in mils which is approximately equivalent to where f is the desired frequency in megacycles, and reducing the dimension along a Z-axis until the desired frequency is obtained and other modes of frequency response related to length and width are caused to disappear.

l1. A piezo-electric quartz element free to oscillate at one frequency only other than its thickness frequency, the first said frequency being a function of the two larger dimensions of said element and having a value, measured in megacycles, which is in the neighborhood of where d equals one of said two larger dimensions measured in thousandths of an inch along a Y- axis.

l2. A piezo-electric quartz element having electrode faces perpendicular to an electric axis and having a single freedom of oscillation the frequency of which is a function of its dimensions along Y- and Z-axes, said element having an optimum response characteristic which is obtained by suitably predetermining the ratio of its length to its width.

13. A piezo-electric element so cut from a natural quartz crystal that its longest dimension is along a Y-axis, its thickness dimension is measured along an X-axis, and its width dimension when measured along an optical axis bears a ratio of less than substantially .7 to the Y-axis dimension for enabling the element to oscillate at one length-mode frequency only.

SAMUEL A. BOKOVOY. 

